A new procedure for nonlinear dynamic analysis of structures under seismic loading based on equivalent nodal secant stiffness. (English) Zbl 1535.74538
Summary: This paper presents a dynamic analysis procedure for predicting the responses of large, highly nonlinear, discontinuous structural systems subjected to seismic loading. The concept of equivalent nodal secant stiffness is adopted to diagonalize the conventional stiffness matrix of the structure. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by the implicit Newmark integration method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. The proposed analysis procedure has the advantages of both the conventional explicit and implicit integration procedures, but with their disadvantages removed. Through extensive applications, the results demonstrate that the proposed procedure is simple and robust for analyzing practical structural systems in terms of computational efficiency and stability.
MSC:
| 74L05 | Geophysical solid mechanics |
Keywords:
dynamic analysis; nonlinear structural system; seismic loading; implicit integration; incremental-iterative procedure; equivalent nodal secant stiffnessSoftware:
SAP2000References:
| [1] | M. J. N. Priestley, Performance based seismic design, in Proc. 12th World Conf. Earthquake Engineering, Paper No. 2831, Auckland, New Zealand (2000). |
| [2] | FEMA P-1050-2, NEHRP Recommended Seismic Provisions for New Buildings and Other Structures, Vol. II: Part 3 Resource Papers (Federal Emergency Management Agency, Washington, 2015). |
| [3] | , Design Specifications of Highway Bridges, Part V Seismic Design (Maruze, Tokyo, 2012). |
| [4] | Ghobarah, A., Performance-based design in earthquake engineering: State of development, Eng. Struct.23 (8) (2001) 878-884. |
| [5] | Clough, R. W. and Penzien, J., Dynamics of Structures, 2nd edn., (McGraw-Hill, Singapore, 1993). |
| [6] | Bathe, K. J., Finite Element Procedures (Prentice-Hall, Englewood Cliffs, New Jersey, 1996). |
| [7] | Chopra, A. K., Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edn., (Prentice-Hall, Englewood Cliffs, New Jersey, 2012). |
| [8] | Chang, S. Y., A new family of explicit methods for linear structural dynamics, Comput. Struct.88 (2010) 755-772. |
| [9] | Chang, S. Y., Comparisons of structure-dependent explicit methods for time integration, Int. J. Struct. Stab. Dyn.15 (3) (2015) 1450055-1-1450055-20. · Zbl 1359.74469 |
| [10] | Yin, S. H., A new explicit time integration method for structural dynamics, Int. J. Struct. Stab. Dyn.13 (3) (2013) 1250068-1-1250068-23. · Zbl 1359.65120 |
| [11] | Rezaiee-Pajand, M. and Hashemian, M., Time integration method based on discrete transfer function, Int. J. Struct. Stab. Dyn.16 (5) (2016) 1550009-1-1550009-22. · Zbl 1359.74440 |
| [12] | Rezaiee-Pajand, M. and Karimi-Rad, M., A new explicit time integration scheme for nonlinear dynamic analysis, Int. J. Struct. Stab. Dyn.16 (9) (2016) 1550054-1-1550054-26. · Zbl 1359.65117 |
| [13] | Bathe, K. J. and Baig, M. M. I., On a composite implicit time integration procedure for nonlinear dynamics, Comput. Struct.83 (2005) 2513-2524. |
| [14] | Bathe, K. J., Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme, Comput. Struct.85 (2007) 437-445. |
| [15] | Bui, Q. V., Modified Newmark family for non-linear dynamic analysis, Int. J. Numer. Methods Eng.61 (2004) 1390-1420. · Zbl 1075.70503 |
| [16] | Kuo, S. R., Yau, J. D. and Yang, Y. B., A robust time-integration algorithm for solving nonlinear dynamic problems with large rotations and displacements, Int. J. Struct. Stab. Dyn.12 (6) (2012) 1250051-1-1250051-24. · Zbl 1359.70003 |
| [17] | Kim, W. and Reddy, J. N., An improved time integration algorithm: A collocation time finite element approach, Int. J. Struct. Stab. Dyn.17 (2) (2017) 1750024-1-1750024-38. · Zbl 1535.74643 |
| [18] | Gravouil, A. and Combescure, A., Multi-time-step explicit-implicit method for non-linear structural dynamics, Int. J. Numer. Methods Eng.50 (2001) 199-225. · Zbl 0998.74033 |
| [19] | Jia, C., Leng, Z., Li, Y., Xia, H. and Liu, L., Partitioned integration method based on Newmark’s scheme for structural dynamic problems, Int. J. Struct. Stab. Dyn.16 (1) (2016) 1640009-1-1640009-16. · Zbl 1359.65110 |
| [20] | Yang, Y. B. and Chiou, H. T., Rigid body motion test for nonlinear analysis with beam elements, J. Struct. Eng.117 (4) (1991) 1053-1069. |
| [21] | Yang, Y. B., Lin, S. P. and Chen, C. S., Rigid body concept for geometric nonlinear analysis of 3D frames, plates and shells based on the updated Lagrangian formulation, Comput. Methods Appl. Mech. Eng.196 (7) (2007) 1178-1192. · Zbl 1173.74450 |
| [22] | Belytschko, T. and Hsieh, B. J., Non-linear transient finite element analysis with convected co-ordinates, Int. J. Numer. Methods Eng.7 (3) (1973) 255-271. · Zbl 0265.73062 |
| [23] | Rice, D. L. and Ting, E. C., Large displacement transient analysis of flexible structures, Int. J. Numer. Methods Eng.36 (9) (1993) 1541-1562. · Zbl 0778.73074 |
| [24] | Crisfield, M. A. and Moita, F. G., A co-rotational formulation for 2-D continua including incompatible modes, Int. J. Numer. Methods Eng.39 (15) (1996) 2619-2633. · Zbl 0883.73076 |
| [25] | Battini, J. M., A non-linear corotational 4-node plane element, Mech. Res. Commun.35 (6) (2008) 408-413. · Zbl 1258.74199 |
| [26] | Borst, R., Crisfield, M. A., Remmers, J. J. C. and Verhoosel, C. V., Nonlinear Finite Element Analysis of Solids and Structures, 2nd edn. (John Wiley & Sons, West Sussex, 2012). · Zbl 1300.74002 |
| [27] | Lee, T. Y., Chung, K. J. and Chang, H., A new implicit dynamic finite element analysis procedure with damping included, Eng. Struct.147 (2017) 530-544. |
| [28] | Shames, I. H., Engineering Mechanics, Vol.IIDynamics, 3rd edn. (Prentice-Hall, New Jersey, 1980). |
| [29] | Bathe, K. J. and Wilson, E. L., Stability and accuracy analysis of direct integration methods, Earthq. Eng. Struct. Dyn.1 (3) (1973) 283-291. |
| [30] | Bathe, K. J. and Noh, G., Insight into an implicit time integration scheme for structural dynamics, Comput. Struct.98-99 (2012) 1-6. |
| [31] | University of California at Berkeley, SAP2000, Integrated Finite Analysis and Design of Structures, Analysis Reference Manual (Version 11.0.8), (Computers and structures, Inc., California, USA, 2007). |
| [32] | H. Chang, Geometrically nonlinear dynamic analysis with plane solid elements, Master thesis, National Central University, Taoyuan (2016) (in Chinese). |
| [33] | C. R. Chen, An analysis method for simulating the ultimate collapse of bridges, Master thesis, National Central University, Taoyuan (2016) (in Chinese). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
